His move was followed by Diana Johnson, who tweeted "I have now written to Jeremy Corbyn to resign as a Shadow Foreign and Commonwealth Office minister."
Perkins and Johnson were accompanied by Shadow Minister for Civil Society Anna Turley, who said in a letter to Corbyn that "the Leadership is not in touch with the hopes, fears and aspirations" of her constituents.
Shadow Minister for Housing and Planning Roberta Blackman-Woods is also reportedly threatening to resign if Corbyn stays as a party leader.
Calls inside the party for a change of leadership grew louder this week after Britain voted on Thursday to quit the European Union. Jeremy Corbyn, who had campaigned for the Remain camp ahead of the referendum, could face a vote of no confidence.
On Sunday, 11 ministers of the shadow cabinet resigned in a mass walkout that was triggered by Corbyn’s decision to sack Shadow Foreign Secretary Hilary Benn.
Meanwhile, at least seven shadow cabinet ministers have so far voiced their support of the embattled party leader, with Shadow Chancellor John McDonnell warning it was the time for the opposition to hold together.